A349741 a(n) = Product_{k=1..n-1} phi(gcd(n,k)).

1, 1, 1, 1, 1, 2, 1, 2, 4, 4, 1, 32, 1, 6, 256, 16, 1, 96, 1, 1024, 2304, 10, 1, 16384, 256, 12, 2304, 13824, 1, 524288, 1, 2048, 102400, 16, 5308416, 14155776, 1, 18, 589824, 134217728, 1, 63700992, 1, 1024000, 86973087744, 22, 1, 8589934592, 46656, 1310720

Offset: 1

Author

Ilya Gutkovskiy, Nov 28 2021

Keywords

• nonn

Crossrefs

Cf. A000010, A001088, A029935, A029940, A046022 (positions of 1's), A051190.

Programs

Mathematica

Table[Product[EulerPhi[GCD[n, k]], {k, 1, n - 1}], {n, 1, 50}]

PARI

a(n) = prod(k=1, n-1, eulerphi(gcd(n, k))); \\ Michel Marcus, Nov 28 2021

Formula

a(n) = Product_{d|n, d < n} phi(d)^phi(n/d).